Two-dimensional flow of chemically reactive viscoelastic fluids with or without the influence of thermal convection

Shear and temperature induced dynamics of a viscoelastic liquid is investigated with direct numerical simulations. A numerical algorithm based on the finite difference method is implemented in time and space with the Oldroyd-B constitutive model for the viscoelastic liquids. The temperature effects are modeled by a combination of Arrhenius kinetics and thermal convection. The standard approach which applies periodic boundary conditions is replaced by one in which the unprescribed boundary values are regenerated from the main flow. The algorithm is validated against well-known Newtonian natural convection flow results. The results show that progressive viscoelasticity leads to lower temperature increases within the fluid system, and that the highest temperature increases are recorded for corresponding Newtonian fluids.